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Search: id:A001785
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| A001785 |
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Second order reciprocal Stirling number (Fekete) [[2n+4, n]]. The number of n-orbit permutations of a (2n+4)-set with at least 2 elements in each orbit. Also known as associated Stirling numbers of the first kind (e.g. Comtet).
(Formerly M5382 N2338)
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+0
4
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| 1, 120, 7308, 303660, 11098780, 389449060, 13642629000, 486591585480, 17856935296200, 678103775949600, 26726282654771700, 1094862336960892500, 46641683693715610500, 2066075391660447667500, 95122549872697437090000
(list; graph; listen)
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OFFSET
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1,2
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 256.
A. E. Fekete, Apropos two notes on notation, Amer. Math. Monthly, 101 (1994), 771-778.
C. Jordan, On Stirling's Numbers, Tohoku Math. J., 37 (1933), 254-278.
C. Jordan, Calculus of Finite Differences. Budapest, 1939, p. 152.
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FORMULA
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[[2n+4, n]]=sum((-1)^i*binomial(2n+4, 2n+4-i)[2n+4-i, n-i] where [n, k] is the unsigned Stirling number of the first kind.
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MAPLE
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with(combinat):s1 := (n, k)->sum((-1)^i*binomial(n, i)*abs(stirling1(n-i, k-i)), i=0..n); for j from 1 to 20 do s1(2*j+4, j); od;
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CROSSREFS
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Cf. A000907, A000483, A001784.
Sequence in context: A055213 A035190 A035815 this_sequence A156411 A076005 A104592
Adjacent sequences: A001782 A001783 A001784 this_sequence A001786 A001787 A001788
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
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More terms, Maple program, formula from Barbara Haas Margolius (margolius(AT)math.csuohio.edu), Dec 14 2000
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